Shaken lattice as a service

ABSTRACT

A shaken-lattice station and a cloud-based server cooperate to provide shaken lattices as a service (SLaaS). The shaken-lattice station serves as a system for implementing “recipes” for creating and using shaking functions to be applied to light used to trap quantum particles. The cloud-based server acts as an interface between the shaken-lattice station (or stations) and authorized users of account holders. To this end the server hosts an account manager and a session manager. The account manager manages accounts and associated account-based and user-specific permissions that define what actions any given authorized user for an account may perform with respect to a shaken-lattice station. The session manager controls (e.g., in real-time) interactions between a user and a shaken-lattice station, some interactions allowing a user to select a recipe based on results returned earlier in the same session.

BACKGROUND

Interferometry is a technique which uses the interference ofsuperimposed waves to extract information. Interferometry typically useselectromagnetic waves and is an important investigative technique in thefields of astronomy, fiber optics, engineering metrology, opticalmetrology, oceanography, seismology, spectroscopy (and its applicationsto chemistry), quantum mechanics, nuclear and particle physics, plasmaphysics, remote sensing, biomolecular interactions, surface profiling,microfluidics, mechanical stress/strain measurement, velocimetry,optometry, and holography. In most interferometers, light from a singlesource is split into two beams that travel in different optical paths,and which are then combined again to produce interference. The resultinginterference fringes give information about the difference in opticalpath lengths.

The precision achievable in interferometry is ultimately limited by thewavelength of the interfering waves, with shorter wavelengths providinghigher precision. Visible light wavelengths range from 400 nm to 700 nm.Ultraviolet light extends the range to 10 nm at the low end; X-raysextend the range down to 10 picometers (pm), while gamma rays havewavelengths around 1 pm. However, exposure to ionizing radiation such asextreme ultraviolet, X-rays, and gamma rays can be problematic,especially as they are a health hazard, causing radiation sickness, DNAdamage and cancer.

Particles of matter, e.g., atoms, have de Broglie wavelengths in thepicometer range and below, making them promising alternatives toionizing radiation for picometer precision interferometry, with heavierparticles having shorter de Broglie wavelengths and thus offeringgreater precision. In fact, interferometers have been developed usingneutrons, atoms, and polyatomic molecules.

A challenge for interferometers based on particles of matter has been todevelop counterparts to the mirrors and beamsplitters used inlight-based interferometers to split, redirect, and combine light beams.In the “shaken-lattice” approach to controlling matter particles, e.g.,neutral atoms, are trapped and cooled in an optical lattice. The opticallattice, which includes a grid formed using an intersection of two pairsof counterpropagating and interfering laser beams, is then shaken; inother words, the phases and/or frequencies of the beams forming thelattice are modulated according to a “shaking” function so that theparticles split, propagate, reflect, and recombine without the use ofadditional beams and (Raman or Bragg) pulses.

Unfortunately, the high acquisition cost and the high-level of expertiserequired to operate shaken-lattice systems, which typically includeparticle (e.g., rubidium and cesium atom) sources, ultra-high vacuum(UHV) systems, laser systems, magnetic systems (i.e., systems forproducing and controlling magnetic fields), and electronics foroperating the laser and magnetic systems, constrains their availabilityfor research and development.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic illustration of a shaken lattice as a service(SLaaS) system.

FIG. 2 is a flow chart of an SLaaS process.

FIG. 3 is a schematic illustration of a SL station of the system of FIG.1 .

FIG. 4 is a screen shot of a graphic user interface of the SLaaS systemof FIG. 1 .

FIG. 5 is a schematic illustration of an account manager data structurefor an account manager of the SLaaS system of FIG. 1 .

FIG. 6 is a schematic illustration of a session manager data structurefor a session manager of the SLaaS system of FIG. 1 .

FIG. 7 is a schematic diagram of a shaken-lattice matched filter systemimplementable using the SLaaS system of FIG. 1 and in other systems.

DETAILED DESCRIPTION

The present invention provides for Shaken Lattice-as-a-Service (SLaaS)in that account holders can operate a shaken-lattice installationremotely via the Internet or other network. The present inventionfurther provides for real-time, exclusive, interactive production and/ormanipulation of shaken lattices and their contents. SLaaS allows accountholders access to shaken lattices without the burden of purchasing andmaintaining the associated equipment. Furthermore, potential purchasersof the equipment are provided a way to evaluate the equipment prior topurchase. Thus, the invention allows more people to study and to developapplications based on shaken lattices.

As shown in FIG. 1 , a shaken lattice as-a-service (SLaaS) system 100includes a set 102 of shaken-lattice stations and a cloud-based SLaaSserver 104. Set 102 includes one or more shaken-lattice stationsincluding representative shaken-lattice-station 106. Shaken-latticestation 106 includes a particle supply 108, recipe hardware 110including a machine-learning engine 111, a controller 112, aquantum-state capture system 114, and a server interface 116.

Particle supply 108 can, for example, supply rubidium 87 (⁸⁷Rb) atoms,which can assume different quantum states depending on the excitationlevel of its single-electron outer shell. When cooled to a sufficientlylow temperature, as determined by a phase-space density, a cloud of ⁸⁷Rbatoms can form a Bose-Einstein condensate in which the atoms share acommon quantum state. Depending on the embodiment, a particle supply canprovide exactly one type of quantum-state carrier or plural types ofquantum state carriers (e.g., potassium and cesium).

Recipe hardware 110 is used to process supplied quantum particlesaccording to a recipe. The processing can include cooling, transport,and inducing phase and/or state transitions. The hardware forshaken-lattice-station 106 can include a vacuum system, a laser system,optical path elements, a magnetics system, and an electronics system. Inaddition, recipe hardware 110 includes a machine-learning engine for usein developing new shaking function recipes and other recipes. Thecomponents of these systems can overlap; for example, an atom chip canserve as part of a vacuum boundary, conduct currents to form magneticfields, and include a window for optical access to the vacuum interior.In other embodiments, e.g., involving an all-optical BEC, there is noatom chip. A controller 112, which may be integrated into theelectronics system, coordinates the hardware actions to implement arecipe received over server interface 116 from SLaaS server 104.

Quantum-state capture system 114 captures observables of quantumparticles to yield wavefunction characterizations. In fact, a recipe canspecify which observables are to be captured, as well as how the captureis to be effected. For example, a fluorescence or absorption image ofatoms may be captured to characterize a wavefunction (or spatialdistribution) of the atoms. The captured observables data, either ascollected or in modified form, is transmitted back to a user via SLaaSserver 104.

Not all information that might be returned to a user qualifies as a“wavefunction characterization”. For example, if an atomic clock returnsa time to a user, that time does not qualify as a wavefunctioncharacterization because it is not descriptive of a quantum state. Inthe case of a BEC, data specifying the number of thermal atoms leftafter BEC production may not qualify as a wavefunction characterizationsas it does not include information descriptive of the quantum state ofthe BEC. However, the time or the number of thermal atoms could qualifyas “based on a wavefunction characterization”.

SLaaS server 104 includes a station interface 120, an account manager122, a session manager 124, a device interface 126, and a recipe library128 of recipes 129. Recipes 129 can include shaking functions 130 (forcases in which an existing shaking function is available) andmachine-learning algorithms 131 (for when a new shaking function isrequired). Recipes 130 and 131 can be based on the teachings in:“Adaptive quantum signal processor” by Evan Salim and Dana ZacharyAnderson, US Patent Publication US2022/0012618A1; and “Atominterferometry using a shaken optical lattice” by C. A. Weidner et al,Physical Review A 95, 043624 (2017) both of which are incorporatedherein in full by reference.

Account manager 122 manages accounts of individual users and corporateentities; this includes managing financial transactions with accountholders 130, which determine permissions for each account. In addition,account manager 122 serves to identify, authenticate, and managepermissions of authorized users for each account holder, e.g.,authorized users 132 of account holder 134.

Account manager 122 can provide for a variety of account types. Forexample, accounts can provide for on-demand access, scheduled access,and stand-by access. On-demand access provides priority access pendingcompletion of a currently implementing recipe and any on-demand recipesin the queue ahead of the current one. Scheduled access means access ata future time from a choice of times offered by the session manager andsubject to change due to conflicts with higher-priority recipes.Stand-by access means that the recipe will be executed when time isavailable; the user will be notified when results are available. Anaccount holder may grant some of its authorized users, e.g., systemadministrators, all the permissions associated with the account type,while it may grant others of its authorized users more restricted setsof permissions.

Authorized users can access SLaaS server 104 via respective user devices140, which include, but are not limited to, computers and mobiledevices. User device 142, for example, includes a graphical userinterface 144 and a network interface 146. Graphical user interface 144provides functionality for recipe creation and/or selection 144, andrecipe transmission 152.

An authorized user can select recipes either directly from recipelibrary 128 on SLaaS server 104 or from a local recipe library on a userdevice 142. The latter library can be updated using entries in cloudrecipe library 128 or by storing recipes created on the user device bythe user. Recipes in library 128 may be selectively forbidden to usersbased on the respective account and user permissions; for example, auser may be able to access shaking functions 130, but notmachine-learning algorithms 131 (which could be used to generate newshaking functions). The recipes can include: unitary recipes 172 thatprovide for exactly one recipe request in a session, and multi-recipes174 that provide for a series of requests allowing a user to see theresult of a first portion of a recipe before deciding to proceed on asecond or subsequent portion of a multi-recipe. A user with sufficientpermissions can create a multi-part recipe by combining unitary recipesor combining at least one unitary recipe with at least one multi recipe.

Herein, an “online session” can include a series of user requests (e.g.,recipe transmissions) and responses (observables generated byimplementing a recipe) during which the user retains continuousreal-time access to a shaken lattice station. An “offline session”involves implementing a recipe while the user is offline (as when arecipe submitted by the user is implemented on a stand-by basis or on anunattended scheduled basis). Session manager 124 of SLaaS server 104tags the received recipe with a session identifier so that any resultsof the recipe can be returned to the correct device and user.

In addition, session manager 124 uses the tag to maintain inter-cyclecontinuity among plural session cycles, i.e., recipe-resulttransactions, where such multiple transactions are permitted (e.g., bythe permissions associated with the account and the user). SLaaS server104 forwards tagged recipes from station interface 120 to serverinterface 116 of BEC-station 106 (or other station). Observablescaptured during recipe implementation are returned to SLaaS server 104,which forwards the observables to the device that originated the recipe.GUI 144 for the device can display the observables data as appropriate,e.g., as images, graphs, tables, etc.

SLaaS system 100 provides for different session types includingsingle-cycle sessions, automated multi-cycle sessions, and interactivemulti-cycle sessions. Single-cycle sessions 172 typically implementunitary recipes 174. Herein, a “recipe” is a document specifying initialconditions and procedures for yielding a result, typically in the formof a quantum wavefunction or a characterization of a quantumwavefunction. For example, a recipe for a Bose-Einstein condensate wouldspecify the equipment and initial state of a shaken-lattice station aswell as the operations required to determine and/or execute a shakingfunction using that shaken-lattice-station. A single-cycle sessiontypically terminates once the result, e.g., an interferometrymeasurement, is reported to the user.

Multi-cycle sessions permit additional procedures to be performed aftera result is reported. In the case of automated multi-cycle sessions, theprocedures follow results without user intervention. Automatedmulti-cycle sessions 176 can implement linear multi-part recipes 178,which provide no choices to be made regarding which procedures are to beimplemented regardless of results, and automated branched multi-partrecipes 180 for which procedures following results are selectedautomatically, e.g., by the session manager based on the results. In anautomated multi-cycle session, results may be reported to the sessionmanager each cycle; these results may be forwarded to the user oraggregated so that only the aggregate result is forwarded to the user atthe end of the session.

Herein, a “branched” recipe is a recipe that includes alternativeprocedures to be selected based on a condition, which may be a resultfrom a previous part or a procedure of the recipe, a user input, or someother factor (e.g., time). Branched recipes that condition a selectionof alternative procedures on a user input after the respective sessionbegins are termed “interactive”, whereas recipes that do not accept suchinput are termed “automated”.

Interactive multi-cycle sessions 182 can provide users with real-time,exclusive, and interactive access to a shaken-lattice-station.Interactive branched multi-part recipes 184 permit users to selectbetween/among branches, taking into account results from previous cyclesin the session. In the case of such interactive recipes, the user'schoices are specified and limited at the outside by the recipe. In thecase of real-time generated recipe sequence 186, the user's choices arenot limited by the first recipe requested. However, follow-up recipesmay be constrained to initial conditions that match the end conditionsof a previous cycle, so the user's choices are not unlimited.

An SLaaS-process 200 is flow charted in FIG. 2 . At 201, an authorizeduser creates and/or selects a first recipe and transmits it to a SLaaSserver. At 202, an account manager running on the SLaaS serverauthenticates the user and identifies the permissions applicable to thatuser. These permissions are those associated with the account that havenot been excluded for use by the present user or the present user's rolein the account holder.

At 203, a session manager running on the SLaaS server checks theapplicable permissions, authorizes the recipe (if it qualifies given thepermissions), tags the recipe with a session identifier, and routes thetagged recipe to a compatible shaken-lattice-station. For example, ifthe recipe calls for the use of ⁸⁷Rb atoms, the session manager canroute the recipe to a shaken-lattice-station set up with an ⁸⁷Rb source,rather than to, for example, a shaken-lattice-station set up with only a¹³³Cs source. More specifically, the selected shaken-lattice station andits current state are to be compatible with the first recipe; in theillustrated embodiment, the session manager rejects a subsequent recipethat is incompatible with the selected shaken-lattice-station. In analternative embodiment, a subsequent recipe requested in the samesession may be routed to a different shaken-lattice-station compatiblewith the subsequent recipe.

At 204, the selected shaken-lattice-station then implements a first(n=1) recipe or part of a multi-part recipe, captures first observablesshaken-lattice data, and transmits a station response to the sessionmanager, the station response being based on the observables data. Thecapturing may be destructive or non-destructive. For example, manyimaging techniques impact the quantum state of the quantum-statecarriers; however, there are dispersive phase-contrast imagingtechniques that are non-destructive. At 205, the session manager thenforwards the first observables data to the user for display on the GUIof the user device. More precisely, the session manager transmits aserver response based on the station response and, thus, based on theobservables data. In some automated multi-cycle sessions implementingmulti-part recipes, observables data is not sent to the user each cycle,but rather data collected over multiple cycles is accumulated and sentcollectively to the user, e.g., at the end of the session.

Commonly, the sessions are unitary recipe (N=1) sessions, in which case,the session manager ends the session at 206 once the first observablesdata is sent to the user device. The session may also end due to atime-out or a user request for disconnection. However, certain premiumaccounts provide for multi-cycle sessions. In such a case, process 200proceeds from action 205 to a virtual action 207 of incrementing n, thatis n→n+1.

How process 200 proceeds from 207 depends on the type of multi-cyclesession. In the case of an automated multi-cycle session implementing alinear or automated branched multi-part recipe, the session returns to204 to implement a next, nth, part of a multi-part recipe, and proceedsfrom there to 205. In the case of an interactive multi-cycle session,the session proceeds to 208 to select a next, nth, recipe or recipepart, in some cases based on prior results.

In the case of an interactive multi-cycle session that allows a user togenerate a recipe sequence in real-time, that is, as the sessionprogresses, the user selects a next, nth, recipe at 208, e.g., based onresults from earlier cycles in the session. The newly selected recipe isthen, in effect, vetted as the session returns to 203 and proceeds from203 to 204 and 205, and so on. Typically, but not in all cases, theshaken-lattice-station selected at 203 is the same across cycles of asession.

In the case of an interactive multi-cycle session implementing aninteractive branched multi-part recipe, the choices made by a user at208 can be constrained to pre-approved recipe parts. After the userselects an nth recipe part, the session can proceed from 208 directly to204, bypassing vetting at 203. The session can then proceed to 205 andso on until completion.

In the event that the data captured at the most recent capture (action204) is non-destructive, the next recipe or recipe part can use, as astarting point, the state involved in that capture. If the data captureis destructive, the next recipe can use a state prior to the capturestate as a starting point. For example, the system can be reinitialized,and the recipe can start with the release of a new population ofrubidium atoms or other quantum-state carriers. Alternatively, anearlier recipe may have left a reservoir of (e.g., pre-cooled)molecules, so the next recipe can begin by drawing a new population fromthe reservoir (instead of returning to the molecule supply).

Consider a user that desires to tune BEC-production parameters toachieve a BEC with a target numerosity (number of atoms, in this case)before using the BEC in an atomtronic transistor or shaken lattice.Because conditions within a shaken-lattice-station may degrade orotherwise change with intervening time and usages, it may not suffice torely on tunings developed in previous sessions. A multi-recipe sessionallows BEC production parameters to be tuned at nearly the same time asthe usage and without intervening sessions. Such real-time, exclusiveand interactive usage of a shaken-lattice station thus providessignificant advantages over multiple single-recipe sessions. Herein, amulti-cycle session would not be considered “exclusive”, if another'suser session altered a quantum state achieved during the session.

Shaken-lattice station 106, shown in greater detail in FIG. 3 , includesa pair of ⁸⁷Rb sources 302, a vacuum system 304, a laser system 306, amagnetics system 308, an imaging system 310, and an electronics system312. Vacuum system 304 includes a pre-cooling cell 322 and a cold cell324, which is capped by an atom-chip 326 that forms part of the vacuumboundary for vacuum system 304. Electronics system 312 includescontroller 112, server interface 116, and power supply 330. Sources 302serve as quantum particle supply 108 (FIG. 1 ). Recipe hardware 110(FIG. 1 ) includes vacuum system 304, laser system 306, magnetics system308, and power supply 330. Imaging system 310 forms part of observablesdata capture system 116 (FIG. 1 ). Shaken-lattice station 106 can be aturnkey system such as the QuCAL Ultracold Atom laboratory availablefrom ColdQuanta, Inc., Boulder Colorado.

Source 302 for shaken-lattice station 106 includes two modules filledwith rubidium 87 (⁸⁷Rb). Other cold-molecule-type BEC-stations caninclude modules filled with cesium 133 (¹³³Cs) and/or filled withpotassium 39 (³⁹K). ⁸⁷Rb, ¹³³Cs, and ³⁹K are alkali elements with asingle electron in their respective outer shells. Alternative sourcematerials can include isotopes of these elements, such as ⁸⁵Rb, alkalineearth metals such as strontium, other elements, and various polyatomicmolecules, other bosons and fermions. In some embodiments, ashaken-lattice station can be configured with two or more sourcematerials, e.g., for comparisons across source materials. Differentsource materials may require different laser frequencies and thus, insome cases, additional lasers.

In shaken-lattice station 106, ⁸⁷Rb atoms can be released into a vacuumby heating one of the source modules. The heating can be effected usingresistive heating generated by driving a current through a resistiveelement in or on the module. Alternatively, a laser can be used to heatthe module and/or its contents. The vacuum into which the atoms arereleased is maintained by a multi-stage vacuum system 304. Releasedatoms travel, e.g., upwards, through one or, in other embodiments, morepre-cooling cells to a cold cell, which, in FIG. 3 , is capped by anatom chip 326. In various embodiments, reservoirs of pre-cooledquantum-state carriers can be formed in one or more of these cells. Atomchip 326 has a split-wire waveguide design and an integrated opticalwindow respectively for magnetic trapping and thru-chip optical accessto trap ultracold atoms.

Vacuum system 304 can include an ion pump and getter materials tomaintain the vacuum conditions within the cells. Vacuum system 304 caninclude opto-mechanical elements for two-dimensional andthree-dimensional laser cooling, optical pumping, and optical probingfor time-of-flight or in-situ imaging. In addition, vacuum system 304can include a photo-optical imaging and projection system, e.g., with a0.6 NA (numerical aperture) primary objective lens. There is also atwo-dimensional acousto-optic beam deflector (2D AOD) to create dynamictwo-dimensional optical potentials projected onto trapped atoms.

The (e.g., upward) movement of the atoms is primarily controlled bylaser system 306. Laser system 306 includes three 780 nanometer (nm)Distributed Bragg Reflector (DBR) diode lasers respectively serving asmaster, cooling slave, and repump slave. In addition, there is a taperedamplifier to increase laser power for cooling. All lasers haveassociated current drivers, 1- or 2-stage temperature controllers, aswell as laser current locking electronics for Doppler-free saturatedabsorption spectroscopy locking to atomic transitions and offset phaselocking to the master laser. By controlling the offset frequency fromthe master laser, the cooling slave also achieves pump and probefunctionality. Additionally, four acousto-optic modulators provide forlaser frequency agility (detuning) and fast (˜nanosecond) intensitymodulation. In addition, there are six optical shutters for binary ONand OFF operation. A blue-detuned 760 nm semiconductor laser providesfor repulsive optical potentials. The lasers are used to manipulateinternal states, cool, guide, move, trap, and image the atoms. Inparticular, they can be used to form lattices to trap and motivate atomsas the laser beams are frequency and phase modulated in accordance withshaken-lattice concepts.

Atom chip 326 can be used to form a magnetic trap. In alternativeembodiments, optical traps are used instead of or in addition to themagnetic trap produced by an atom chip (e.g., to trap a BEC). Thus, someembodiments dispense with an atom chip; completing the vacuum boundarywith a glass or silicon wall as part of the vacuum boundary.

Laser system 306 cooperates with magnetics system 308 to definetwo-dimensional and three-dimensional magneto-optical traps (MOTs) andlattices. Magnetic system 308 includes permanent magnets around thepre-cooling cell and copper electromagnetic field coils including x-,y-, z-bias coils and a quadrupole transport coil around the cold cell;current through these coils generates magnetic fields that help form theMOT in the cold cell. Imaging system 310 includes two CCD cameras forcharacterizing the atoms in the cold cell: a Basler for time-of-flightimaging and an Andor EMCCD for in-trap imaging.

Controller 112 controls and coordinates the actions of the various othersystems. Controller 112 outputs analog and digital signals to controlthe various systems, e.g., to turn lasers and magnets on and off, and tocontrol currents through atom chip 326. In an alternative embodiment, acontroller includes analog inputs for monitoring and diagnostics, e.g.,photo-diode signals of MOT loading. Controller 112 runs control systemsoftware on National Instruments LabVIEW to create timing files to sendto electronics system 312. Controller 112 includes a NationalInstruments PXI chassis with a real-time environment. Analog and digitaloutput cards connected to the PXI chassis deliver control signals toperipheral electronics. Low-noise current supplies are used forelectromagnetic field coils and the atom chip. An arbitrary waveformgenerator is used to create and execute radio-frequency (RF) waveformsdriving the two-dimensional acousto-optic deflector.

The various systems of a shaken-lattice-station can share components.For example, atom chip 174 forms part of the electronics system, part ofthe magnetics system, and part of the vacuum system. Comparing FIGS. 1and 3 , recipe hardware 110 (FIG. 1 ) includes vacuum system 304, lasersystem 306, magnetics system 308, and electronics system 312 (excludingcontroller 112 and server interface 116). Imaging system 310 (FIG. 3 )is included in observable data capture 114.

From a user's viewpoint, interaction with graphical user interface 144(FIG. 1 ) sends a selected recipe to a shaken-lattice station and theshaken-lattice station returns results, e.g., in the form of awavefunction characterization (quantum-state data descriptive of thephysical state(s)) of the relevant quantum molecules in theshaken-lattice station. The graphical user interface allows userdefinitions of multi-stage shaking function generation recipescontrolling 24 analog and 16 digital control lines. The GUI allowsgraphical visualization or control signal levels (constant, linear ramp,exponential, sinusoid, and user input functions).

Herein, use cases for shaken-lattice station 106 include: basicBose-Einstein condensate (BEC) production, atomtronics, and shakenlattice applications. In the basic BEC use case, a user is given controlover one or more of the following parameters: 1) laser cooling; 2)optical pumping; 3) quadrupole magnetic trapping and transport; 4) atomchip loading; 5) evaporation (final-stage cooling); and 6) atom-chiptrap decompression and imaging. Control of laser cooling can includecontrol over a magneto-optical trap (MOT), a compressed magneto-opticaltrap (CMOT), and polarization gradient cooling (PGC). This controlincludes control over magnetic quadrupole and bias fields, laser tuning,and stage duration. Control over optical pumping can include controlover magnetic bias fields and laser pulse duration. Control overatom-chip loading can include control over magnetic quadrupole and biasfields, current in atom-chip traces, and stage duration. Control overevaporation can include control over bias fields, current in atom chiptraces, radio-frequency knife frequency, radio-frequency knife power,and stage duration. Control over atom-chip trap decompression andimaging can include control over bias fields, current in atom chiptraces, stage duration, time of flight (time between trap release andimage), and probe pulse duration.

Which parameters are presented to a user can depend on account type(e.g., real time accounts, scheduled accounts, stand-by accounts),user/role authorization (e.g., administrators, project managers,technicians), and user selections. Users interested in creating shakingfunctions with specific characteristics or in exploring ways ofoptimizing shaken lattices can be given access to all relevantparameters. Others might be given access to only one parameter, orparameters of a single stage, e.g., the evaporation stage. In the lattercases, the other stages and parameters would be pre-set, e.g.,pre-optimized. In still other cases, a user who wants to use a shakingfunction as a starting point might have access to a preset recipe for ashaking lattice without any access to underlying settings.

At the end of a BEC production cycle, by tuning the variables on theprior chart, the user will have control over the total number N, thetemperature T, and the chemical potential μ of the atoms. Below thecritical temperature, T_(c), there can be N_(c) condensed atoms andN_(th) thermal atoms, so the user also has control over the “condensatefraction”. Given a number of condensed atoms, N_(c), the cloud will havechemical potential μ, that arises due to atomic interactions, inaddition to the thermal energy associated with temperature T. Chemicalpotential depends on the trap “tightness” characterized by the atom-chiptrap frequencies, which can be controlled by current in the chip tracesand by adjusting the bias field strength.

As shown in FIG. 4 , graphical user interface (GUI) 144 for a computeris shown presenting, to a user, controls for time-of-flight (e.g., timeafter atoms are released from the trap) and for atom temperature T. Aslider 402 offers a selection from 5 to 25 milliseconds (ms) fortime-of-flight; the user has selected 20 ms. At ultracold temperatures,a larger time of flight is required to accurately extract thermodynamicproperties of the atoms. A slider at 404 offers a selection of atomictemperature from cold to hot by tuning the RF knife frequency from 2.61MHz to 2.70 MHz, relative to the trap bottom at 2.60 MHz; in the exampleof FIG. 4 , the user has selected 2.63 MHz. Tuning the RF knifefrequency nearer to the trap bottom produces pure BECs, while partiallycondensed clouds are produced for larger RF knife frequencies.Activating (clicking on) a run button 406 causes a BEC with the selectedtemperature to be produced by shaken-lattice-station 106.

A florescence image 410 is taken at the selected time (20 ms after anoptical trap is released). Fluorescence image 410 is processed to yielda best-fit image 412. Depending on the embodiment, the best-fit imagesand graphs might be generated by the shaken-lattice station 106, theSLaaS-server 104, or an app. Graphs 414 and 416 representing anx-dimension slice and ay-dimension slice, respectively, are alsoprovided. In addition, a table 418 specifying numbers of atoms(numerosities) is displayed in the GUI. According to the population datarepresented in FIG. 4 , there are 9076 total atoms, 2383 of which belongto the produced BEC, with 6693 atoms remaining thermal. From theseabsolute values, fractional or percentage values (e.g., BEC atoms as apercent of total atoms) can be calculated. GUI 144 can present othercontrols and result representatives, depending on user permissions andpreferences. GUI 144 is designed to operate natively on mobile devices,as well, without loss of functionality.

In the atomtronic use case, a user can control BEC-station 106 tocreate, modify, and/or operate an atomtronic circuit or a circuitelement, e.g., the atomtronic transistor described in: Chapters 7-9 of“Single Atom Delivery into a Bottle Beam Trap Using an Optical ConveyorBelt and Quantum Coherent Gain in a Matterwave Transistor” (available athttps://scholar.colorado.edu/concern/graduate_thesis_or_dissertations/qz20),a Ph.D. thesis by Brad Anthony Dinardo; and “Experimental Realization ofAtomtronic Circuit Elements in Non-Equilibrium Ultracold Atomic Systems”(available athttps://scholar.colorado.edu/concern/graduate_thesis_or_dissertations/rr171x224),a Ph.D. thesis by Seth C. Caliga.

Atomtronic circuits are defined by optical potentials that section offdifferent portions of the atomic trap waveguide to control the flow ofatoms through the “circuit.” Users can have control over: arbitraryoptical potentials defined by 2D AOD in a high resolution opticalprojection system; number of atoms, chemical potential in various partsof the circuit/device, temperature; and terminator beam on/off—whichcouples atoms out of the circuit to prevent unwanted interference withreflected matter waves at the circuit output. In addition to parametersspecific to the atomtronics use case, the user can be provided controlover the basic BEC parameters.

In the shaken-lattice use case, in addition to controlling theparameters for creating a BEC, the user may be provided with controlover the following parameters: all-optical-BEC formation controls and/oratom-chip trap to optical lattice hand-off parameters; optical latticelight intensity to provide user control over trap depth; and shakingfunction, controlled by user input to a laser phase and/or frequencymodulator. Regarding the lattice light intensity: at low lattice depth,atoms can tunnel between adjacent lattice sites, while at high latticedepth (high intensity) atoms are pinned to each lattice site. Regardingthe shaking function: independent control over each lattice axis allowsarbitrary, uncoupled shaking functions along each axis.

Account manager 122 (FIG. 1 ) includes a data structure 500 shown inFIG. 5 . Account-manager data structure 500 includes an accounts datatable 510, account permissions lists 540, authorized user tables 550,and user permission lists 580. In account data table 510, the recordscorrespond to respective accounts, while the fields correspondrespectively to the following fields: account ID 512, account holdername 514, account-holder credentials 516, account-holder address 518,account type 520, payment plan 522, account start date 524, and accountstatus 526. For each distinct account type, there is a correspondingpermissions list of account permissions 540 of permissions associatedwith accounts of that type.

For each account ID there is a corresponding table of authorized users550, including authorized user table 551. Each record of an authorizeduser table corresponds to a respective user authorized by the respectiveaccount holder to access SLaaS system 100. For each authorized usertable, the records correspond to respective authorized users, while thefields include: user ID 552, account ID 554 (for reverse lookup), username 556, user credentials 558, user IP address 560, user role 562, userpreferences 564, and user status 566. For each distinct user role(administrator, project manager, senior user, trainee, etc.) there is arespective one of the user permissions lists 550 that defines userpermissions (which can be a subset of the account permissions for thecorresponding account type).

When, at 201, FIG. 2 , a user transmits a first recipe; this correspondsto transmitting a user request as indicated at 602 in FIG. 6 . Theaccount manager extracts from the request, user credentials toauthenticate the user and identify the associated account. The accountmanager looks up the account to ensure it is active and that the user'sauthorization is still active. If everything checks out, the accountmanager forwards the request and a pointer to a user permissions listassociated with the user/role.

Session manager 124 (FIG. 1 ) includes a session-manager data structure600, FIG. 6 , which includes a session table 604, a recipe base 640, astation table 642, and a log base 644. Each user request 602 causessession manager 124 to log records into session table 604. Each recordin table 604 corresponds to a respective session. In some embodiments,there are separate session tables for each account.

The fields for session table 604 are session ID 610 (assigned by sessionmanager 124); device IP address 612 (extracted from request) account ID614 (provided by account manager 122 from field 554 (FIG. 5 ) of usertable 551; user ID 616 (provided by account manager 122 from field 552(FIG. 5 ) of user table 551; user permission list ID 618 (pointer touser permissions list 580 provided by account manager 122); currentrecipe ID 620 (extracted from original or follow-on request with entryinto recipe base 640; station ID 622 (provided by session manager 124after matching recipe to station types listed in station table 642,which identifies shaken-lattice-stations according to type, e.g.,resident quantum carriers; station address 624; most-recent results 626(forwarded to user at device address); session log ID 628 (pointer to alog in log base 644 for the current session); and session status 630(e.g., active, iteration number, expired). Once session manager 124finds an available shaken-lattice station that matches the requestedrecipe, it tags the recipe with the session ID and forwards the taggedrecipe to the selected shaken-lattice station.

In a matched filter embodiment, a AQSP system serves as a shaken-latticematched filter that finds matches by comparing quantum wavefunctions. Anoptical lattice can be “shaken” by varying the phase or frequencyrelationship between interfering laser beams. The phase changes causethe interference fringes, which define the trap boundaries, to move. Themovement of trap boundaries can be used to manipulate the quantumwavefunction; for example, a stationary population of moleculesdistributed in a lattice can be coherently split into twocounterpropagating populations. One advantage of a shaken-latticematched-filter is that it can be readily integrated into othershaken-lattice instruments, including shaken-lattice interferometers.

The lattices of interest herein are arrays of potential wells formedusing interfering laser beams, in some cases supplemented by magneticfields. The potential wells serve as traps for atoms (or polyatomicmolecules). Herein, “molecule” refers to the smallest particle of asubstance that retains all the properties of the substance and iscomposed of one or more atoms; this definition, which is set forth inthe Merriam Webster Dictionary; encompasses monatomic (single-atom)molecules as well as polyatomic molecules. Thus, gas-phase alkali (e.g.,potassium, rubidium, and cesium) atoms used in embodiments hereinqualify as molecules under this definition. An alternative definitionset forth in the IUPAC Gold Book, “An electrically neutral entityconsisting of more than one atom”, is not used herein.

The matched filter aspires to detect matches between signals that havethe same effect on molecules in a lattice when used as shaking functionsfor the lattice that confines the molecules. However, not all signalsimpact the wavefunction of the molecules. Accordingly, the presentinvention calls for combining signals of interest with a controlfunctions to yield a recipe function that results in a desired effect onthe wavefunction of molecules entrained in an optical lattice.

For example, a shaken-lattice matched-filter system 700, shownschematically in FIG. 7 , provides for evaluating respective matches ofsignals S_(s)(t) with a template S_(T)(t), using a shaken latticegenerated by and within a physics system 710. Matched filters are usedto detect signals that match templates (reference waveforms) and haveapplications including in radar, sonar, digital communications, imageprocessing (e.g., of X-Ray images), and gravitational-wave astronomy.Prior-art matched filters include electronic devices that, in effect,convolve the signal with a conjugated time-reversed version of thetemplate.

Physics system 710 includes a pair of lasers 712 and 714 that generaterespective ones of counter-propagating red-detuned laser beams 716 and718. Counter-propagating laser beams 716 and 718 interfere to form an atleast one-dimensional (1D) optical lattice 720. While, in system 700,beams 716 and 718 are output from respective lasers 712 and 714, inalternative embodiments, the output of a single laser is split and theresulting branches are redirected to define counter-propagating beams.

Optical lattice 720 is populated by molecules 722, which are shown attime t=t₀ in an initial quantum state corresponding to an initialwavefunction state Ψ₀, forming a centrally-located cluster 724. In theillustrated scenario, the molecules are monatomic molecules, namely,rubidium 87 atoms. Where the molecules in the lattice are alkali metalor other atoms, they are referred to herein as “atoms”, with theunderstanding that the invention also provides for the use of polyatomicmolecules.

System 700 provides for shaking lattice 720 so that atoms 722 transitionto at least one other state. In the illustrated scenario, atoms 722transition from initial wavefunction state Ψ₀ to a second and finalwavefunction state Ψ_(n), shown in FIG. 1 at time t=t₁. In the case ofend wavefunction Ψ_(n), atoms 722 are split into two clusters 726 and728 located at either side of the lattice center. In general, eachsucceeding state differs from its immediate predecessor; thus, in asingle-transition two-state sequence, the second and final state differsfrom the initial state. However, where multiple state transitions areimplemented, it is possible that the final transition features a returnto an initial state or to some other state that is not its immediatepredecessor.

As explained above, “shaking” of a lattice is effected by varying phasesor frequencies of counter-propagating beams used to form the lattice. Inthe illustrated scenario, beam 716 maintains a constant frequency andphase θ₀, while the phase of beam 718 varies relative to the phase ofbeam 716 according to a time-varying shaking function R(t). Inalternative scenarios, the phases of both of a pair ofcounter-propagating beams can be varied.

Shaken-lattice as a service provides for recipes with previouslydetermined shaking functions as well as recipes for determining shakenlattice functions using machine learning. In the latter case, the usercan be presented with options of different machine-learning algorithms,e.g., to identify the most effect and/or efficient algorithms.

Herein, “observables” refers to linear operators on the Hilbert spacethat constitute the possible states of the quantum system. Eigenvaluesof the system are then real valued quantities such as number, phase,energy, etc. “Observables data”, that is, data characterizing one ormore observables, is returned by a shaken-lattice-station. Thus,observables data can be said to characterize wavefunctions and quantumstates. Results returned to a user can include observables as well assolutions to externally defined problems.

The illustrated embodiments exemplify shaken lattice as a service(SLaaS), that provides cloud access for producing, manipulating, andusing quantum particles in an ultra-high vacuum (below 10-9 Torr). Insome embodiments, ultra-cold temperatures below 1 microKelvin and evenas low as tens of nanoKelvins are achieved. Applications include cloudaccess to shaken-lattice stations for production, manipulation, and useof shaken lattices, quantum sensing, quantum positioning (e.g., fornavigation), quantum signal processing, quantum, information processing,quantum simulation, quantum annealing, algorithmic gate-model quantumoperations, and neutral atom qubit array formation and maintenance.

Neutral atom qubits are generally encoded in environmentally insensitiveelectronic states of atoms. The environmental insensitivity of the qubitstates makes them ideal for long-lived coherent quantum informationstorage but implies that the qubit-qubit interactions required formulti-qubit gate operations are not natively present. A standardapproach is to make use of a third “Rydberg” state in addition to thepair of low-lying states in which the qubit is encoded to generate therequired qubit-qubit interactions for multi-qubit gate operations.

Rydberg states are electronic states with highly excited principlequantum number n. The atom's electric dipole moment scales as n², whichmeans that the interaction between a pair of Rydberg excited atoms willbe strong for large n. The Rydberg-Rydberg interaction is generallydipole-dipole in nature at short distances (<R_(C) microns), scaling asn⁴/R³, and van der Waals at larger distances (>R_(C) microns), scalingas n¹¹/R⁶, where R is the distance between the atoms and R_(C) is acrossover distance between the two scalings that depends on species,state, and the electromagnetic environment. For a variety of parameters,R_(C) lies in the range of a few microns, generally between 1-10microns. Thus, the interaction can be strong for nearby atoms, but stilla weak perturbation for more distant atoms.

Herein, a “quantum particle” is a particle that can assume statescorresponding to eigenvalues, that is, solutions to Schrödinger'sequation and superpositions thereof. Herein, the quantum particles ofinterest include atoms and other molecular entities. Herein, a boson isa subatomic particle the spin quantum number of which has an integervalue (0, 1, 2 . . . ). Bosons form one of the two fundamental classesof subatomic particle, the other being fermions, which have oddhalf-integer spin (½, 3/2 . . . ) Every observed subatomic particle iseither a boson or a fermion. Neutral atoms with an even number ofneutrons are bosons, while those with an odd number of neutrons arefermions. An ideal Bose gas is a quantum-mechanical phase of matter,analogous to a classical ideal gas. It is composed of bosons, which havean integer value of spin, and obey Bose-Einstein statistics. Thestatistical mechanics of bosons were developed by Satyendra Nath Bosefor a photon gas, and extended to massive particles by Albert Einsteinwho realized that an ideal gas of bosons would form a condensate, namelya Bose-Einstein condensate at a low enough temperature, unlike aclassical ideal gas.

Herein, a “shaking function” is a function according to which light usedto form a trap confining quantum particles is phase and/or frequencymodulated so as to manipulate the quantum particles. Herein, “real-time”refers to actions being initiated by a station containing the coldquanta within ten seconds of a user request for those actions.“Exclusive” refers to the prevention of access to a quantum system byusers other than the session owner. “Interactive” refers to actionsbeing taken in response to user requests based on results of previoususer actions in the same session.

Herein, all art labeled “prior art”, if any, is admitted prior art; allart not labeled “prior art”, if any, is not admitted prior art. Theillustrated embodiments, variations thereupon and modifications theretoare provided for by the present invention, the scope of which is definedby the following claims.

What is claimed is:
 1. A shaken lattice as a service (SLaaS) processcomprising: receiving, by a cloud-based server from a first user device,a user request including a program or recipe; sending, by thecloud-based server to a shaken-lattice station, a server request basedon the user request; implementation of the server request by theshaken-lattice station, the implementation including, cooling quantumparticles to cold temperatures in an ultra-high vacuum to provide coldquantum particles, the cold temperatures being less than onemilliKelvin; executing a shaking function so as to modulate a phase orfrequency of light used to form a trap confining the cold quantumparticles; and capturing observables data characterizing a quantum-stateof the cold quantum particles; transmitting, by the shaken-latticestation to the cloud-based server, of a station response to the serverrequest, the station response being based on the observables data; andtransmitting, by the cloud-based server to a second user device, aserver response to the user request, the server response being based onthe station response, the second user device being the same as orseparate from the first user device.
 2. The SLaaS process of claim 1wherein the shaking function is determined prior to the implementation.3. The SLaaS process of claim 1 wherein the shaking function isdetermined using a machine-learning engine during the implementation. 4.The SLaaS process of claim 1 providing for interactive production ormanipulation of the cold quantum particles during a session in which auser selects the recipe or a recipe part of a multi-part recipe based ona characterization of a quantum state of the cold quantum particlesearlier in the session.
 5. The SLaaS process of claim 1 wherein the userrequest includes the recipe that specifies procedures for producing,manipulating, or characterizing the cold quantum particles.
 6. The SLaaSprocess of claim 5 wherein the recipe is a branched recipe definingalternative branches to be taken depending on conditions met.
 7. TheSLaaS process of claim 6 wherein the branched recipe is an interactivebranched recipe, wherein the conditions include a user decision.
 8. TheSLaaS process of claim 1 wherein the cold quantum particles are atoms.9. The SLaaS process of claim 8 wherein the atoms are neutral alkali oralkaline earth metal atoms.
 10. The SLaaS process of claim 1 furthercomprising authenticating, by the cloud-based server, a user.
 11. ABose-Einstein condensate as a service (SLaaS) system comprising: ashaken-lattice station including a controlled environment forimplementation of recipes for altering wavefunctions of cold quantumparticles having a temperature of less than one milliKelvin, theimplementation including a shaking function so as to modulate a phase orfrequency of light used to form a trap confining the cold quantumparticles, a wavefunction characterization system for generating resultseither including characterizations of the wavefunctions or based oncharacterizations of the wavefunctions, and a server interface forreceiving the recipes and for transmitting the results; and acloud-based server including a station interface for transmitting therecipes to and receiving the results from the shaken-lattice station, adevice interface for receiving from user devices requests specifyingrecipes and for transmitting respective results to the user devices, anda session manager for managing interactions between authenticated usersand the shaken-lattice station, the session manager being coupled to thestation interface and the device interface.
 12. The SLaaS system ofclaim 11 wherein the shaking function is determined prior to theimplementation.
 13. The SLaaS system of claim 11 wherein the shakingfunction is determined using a machine-learning engine during theimplementation.
 14. The SLaaS system of claim 11 wherein the cloud-basedserver further includes an account manager for managing accounts, themanaging including managing financial transactions with the accounts andauthenticating users associated with the accounts.
 15. The SLaaS systemof claim 11 providing for interactive production or manipulation of thecold quantum particles during a session in which a user selects therecipe or a recipe part of a multi-part recipe based on acharacterization, received earlier in the session, of a quantum state ofthe cold quantum particles.
 16. The SLaaS system of claim 11 wherein auser request includes the recipe that specifies procedures forproducing, manipulating, or characterizing the cold quantum particles.17. The SLaaS system of claim 16 wherein the recipe is a branched recipedefining alternative branches to be taken depending on conditions met.18. The SLaaS system of claim 17 wherein the branched recipe is aninteractive branched recipe, wherein the conditions include a userdecision.
 19. The SLaaS system of claim 11 wherein the cold quantumparticles are atoms.
 20. The SLaaS system of claim 19 wherein the atomsinclude neutral alkali or alkaline earth metal atoms.